Modelling and control of the motion of a disk rolling on a spherical dome

This work deals with the modelling and control of the motion of a disk rolling without slipping on a rigid spherical dome. It is assumed here that the motion of the disk is controlled by a tilting moment, a directional moment, and a pedalling moment. First, a mathematical model of the motion of the disk rolling on the dome is derived. Then, by using a kind of an inverse control transformation, a control strategy is proposed under which the motion of the disk is stabilized and is able asymptotically to track any smooth trajectory which is located on the spherical dome.